Back to School in STEM: Thinking outside the box on day one in math

There is no doubt that the first day of school is an important one. Although my reputation may proceed me, ultimately, this is the first impression my students will have of me. This is where I get to show expectations: mine for them and them for me. In my secondary math classroom, I like to kick it off with creative problem solving. The purpose of these gold medal style problems on day one is to:

Introduction - After a brief introduction in which I share 3 quick facts about myself (I'm am an ultramarathon runner, I have travelled to 4 different continents, and I love Brussels sprouts), I explain that this is there chance to show me who they are as mathematicians. Later in the first couple of weeks, they will show me who they are as a person (more on that here).

Objective/activity - I reveal the objective (projected on the board): to conquer as many gold medal problems as a group as possible. A minimum of 2 students in each group must be working on any one problem and an individual student can work on no more than 3 problems during the activity. Top prize - Reigning class group for the week. (Champion groups are posted on the leaders' board each week).

Class groups - The make-up of groups matters less in this activity than in others, and I don't know the kids yet. I hand each student a colored puzzle piece when they enter the room. After I explain the activity, students find the other people in their group by completing the puzzle. Four people to a group is ideal, but 5 is workable. Three people tends to be too small.

Let the challenge begin - I distribute 10 gold medal problems. Every group gets the same set of problems but can work on them in any order. I like these problems because they are about creative solutions not just

about mathematical knowledge. Some of them can be solved with algebra such as factorials, but they can all be solved regardless of what students remember from the past years. In this way the problems are flexible enough to be used in classes from Algebra through Calculus. You can find some interesting examples here. I've included a couple of my favorites as well below:

There are 25 horses. What is the minimum number of races you need to find the fastest 3 horses? You can race up to 5 horses at a time, but you do not have a timekeeping device.

Five pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain).The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go "Aye", the loot is divided as proposed, as no pirate would be willing to take on the captain without superior force on their side.If the captain fails to obtain support of at least half his crew (which includes himself), he faces a mutiny, and all pirates will turn against him and make him walk the plank. The pirates start over again with the next senior pirate as captain. What is the maximum number of coins the captain can keep without risking his life?

A king wants his daughter to marry the smartest of 3 extremely intelligent young princes, and so the king's wise men devised an intelligence test.The princes are gathered into a room and seated, facing one another, and are shown 2 black hats and 3 white hats. They are blindfolded, and 1 hat is placed on each of their heads, with the remaining hats hidden in a different room.The king tells them that the first prince to deduce the color of his hat without removing it or looking at it will marry his daughter. A wrong guess will mean death. The blindfolds are then removed.You are one of the princes. You see 2 white hats on the other prince's heads. After some time you realize that the other prince's are unable to deduce the color of their hat, or are unwilling to guess. What color is your hat? Note: You know that your competitors are very intelligent and want nothing more than to marry the princess. You also know that the king is a man of his word, and he has said that the test is a fair test of intelligence and bravery.

Wrapping up - As we get towards the end of class, I gather responses. Winners will be declared the next day unless I am teaching on a block schedule in which we have time to reveal the winning group. I give only a score but not the answers (refer back to purpose). I find that some students love these problems and over the course of the year will solve them on their own as an option during time-fillers.

Until tomorrow - Students are handed the syllabus on the way out. At the beginning of the next class, we have a short quiz on the syllabus. I let them know it is coming. Tomorrow will present their second opportunity to show me what they know!

Thanks for joining us for the blog up.

Stop by on August 6th to see what I'll be doing on the first day of Pre-Calculus this year.

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About Me

I am a research policy advocate, educator, curriculum developer, author, PhD, amateur chef and of course, ultra marathon runner. I am deeply passionate about helping every student have the best opportunity to find their passions and develop their skills.